Probability distributions, expected value, and the spread of a random variable

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari's dot plot shows the chances for the number of seeds that sprout when 3 are planted, using 20 equally weighted dots. What is the chance that at least 2 seeds sprout?

   7/10
2. 2.

   Bo's dot plot shows the chances for the number of goals the class team scores in a game, using 20 equally weighted dots. What is the chance that the team scores at most 1 goal?

   1/2
3. 3.

   Esme's dot plot shows the chances for the number of books a student borrows on one library visit, using 20 equally weighted dots. What is the chance that a student borrows at least 1 book?

   17/20
4. 4.

   Jun's dot plot shows the chances for the number of heads when 3 fair coins are tossed, using 8 equally weighted dots. What is the chance that at most 2 heads land?

   7/8

5. Read this first

   Table

   x = 1, 2, 3, 4, 5; P(x) = 0.3, 0.1, 0.15, ?, 0.05. Dot plot: number line 1 to 5, tick every 1; each stack is as tall as its chance (one dot = 1/20 of the chance).

6. 5.

   Luz writes the probability distribution of how many laps a class runner finishes in 5 minutes, but one chance is missing. What is P(x = 4)?

   0.4
7. 6.

   Table: x = 0, 1, 2, 3; P(x) = 0.05, 0.6, ?, 0.15. Milo writes the probability distribution of how many buses arrive late on a school morning, but one chance is missing. What is P(x = 2)?

   0.2

8. Table

   x = 1, 2, 3, 4, 5; P(x) = 0.12, 0.33, 0.25, ?, 0.08. Dot plot: number line 1 to 5, tick every 1; each stack is as tall as its chance.

9. 7.

   Noah writes the probability distribution of how many stickers come in a surprise sticker pack, but one chance is missing. What is P(x = 4)?

   0.22
10. 8.

    Table: x = 0, 1, 2, 3; P(x) = 0.1, 0.3, 0.4, 0.2; x*P(x) = 0, 0.3, 0.8, 0.6. Ren's table gives the distribution of the number of goals in a class game, with each value times its chance. What is the expected value?

    1.7
11. 9.

    Table: x = 0, 1, 2, 3; P(x) = 0.05, 0.25, 0.4, 0.3; x*P(x) = 0, 0.25, 0.8, 0.9. Zee's table gives the distribution of the number of birds at a feeder in one minute, with each value times its chance. What is the expected value?

    1.95
12. 10.

    Table: x = 2, 3, 4, 5; P(x) = 0.1, 0.25, 0.3, 0.35; x*P(x) = 0.2, 0.75, 1.2, 1.75. Ari's table gives the distribution of the minutes a slide line takes at the park, with each value times its chance. What is the expected value?

    3.9